Ray's New Intellectual Arithmetic · Lesson XVI · Unit 2: Multiplying and dividing

16. Dividing: how many can you buy?

Goal: Your child solves “how many can you buy” and sharing problems, and knows divisor, dividend and quotient.

⏱ About 20 minutes · 5 steps

Open it at the Internet Archive ↗

You'll need

  • The book page (press “📖 Book page”, or use a printed copy)
  • Paper for jotting, though the work is meant to be done in the head

What's in the book

Twenty-six problems answered like “Ans. 4 cakes. Why? Because 1 is contained in 4, four times.” Then the definitions of division, divisor, dividend, quotient and the sign ÷.

The lesson, step by step

  1. Warm up

    Ask three or four problems from the last lesson again, out of order. Your child answers and says why.

  2. Show the reasoning

    SayAt 3 cents each, for 9 cents I can buy as many pears as 3 cents are contained times in 9 cents, which are 3 times. So 3 pears.

    “Contained in” is the book's way of saying “goes into”.

  3. Work the problems aloud

    Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:

    At 3 cents each, how many pears can you buy for 9 cents?

    A boy has 16 marbles and puts them in piles of 2: how many piles?

    Four quarts make 1 gallon: how many gallons in 36 quarts?

  4. Ask “Why?”

    After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.

  5. Wrap up

    Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.

Afterwards

Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.

Answers to the book's problems

1) 4. 2) 2. 3) 3. 4) 4. 5) 2. 6) 3. 7) 5. 8) 7. 9) 3. 10) 8. 11) 6. 12) 4. 13) 7 yd. 14) 11 yd. 16) 5. 17) 9 hr. 18) 7. 19) 10. 20) 8. 21) 7. 22) $6. 23) 9 gal. 24) 4 hr. 25) 7. 26) 5.

Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in Ray's own Key ↗.

@teddyrookbook GitHub